where 0≤dk<k0subscriptdkk0\leq d_{k}<k for some integerNNN. Unlike decimal representations
of fractions and, more generally representations with any fixedbase,
factorial base representations of rational numbers all terminate.

We can also employ a more concise notation as is used in
representing fractions in other bases and simply list
digits after a point. Since we would need an infinite
supply of digits, we make the same compromise as when
writing factorial base representations of integers.
With this convention, we than have the following table
of factorial base representations of fractions.